Anomalous Dissipation, Anomalous Work, and Energy Balance for the Navier--Stokes Equations

2021 ◽  
Vol 53 (4) ◽  
pp. 3856-3887
Author(s):  
Alexey Cheskidov ◽  
Xiaoyutao Luo
Keyword(s):  
Energy Balance ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Anomalous Dissipation ◽  
Work And Energy

scholarly journals Inviscid limit for the damped generalized incompressible Navier-Stokes equations on $ \mathbb{T}^2 $

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yang Liu ◽  
Chunyou Sun
Keyword(s):  
Stokes Equations ◽  
Inviscid Limit ◽  
Navier Stokes ◽  
Dissipative Operator ◽  
Navier Stokes Equations ◽  
Long Time ◽  
Time Averages ◽  
Weaker Conditions ◽  
Anomalous Dissipation

<p style='text-indent:20px;'>In this paper, for the damped generalized incompressible Navier-Stokes equations on <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{T}^{2} $\end{document}</tex-math></inline-formula> as the index <inline-formula><tex-math id="M3">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula> of the general dissipative operator <inline-formula><tex-math id="M4">\begin{document}$ (-\Delta)^{\alpha} $\end{document}</tex-math></inline-formula> belongs to <inline-formula><tex-math id="M5">\begin{document}$ (0,\frac{1}{2}] $\end{document}</tex-math></inline-formula>, we prove the absence of anomalous dissipation of the long time averages of entropy. We also give a note to show that, by using the <inline-formula><tex-math id="M6">\begin{document}$ L^{\infty} $\end{document}</tex-math></inline-formula> bounds given in Caffarelli et al. [<xref ref-type="bibr" rid="b4">4</xref>], the absence of anomalous dissipation of the long time averages of energy for the forced SQG equations established in Constantin et al. [<xref ref-type="bibr" rid="b12">12</xref>] still holds under a slightly weaker conditions <inline-formula><tex-math id="M7">\begin{document}$ \theta_{0}\in L^{1}(\mathbb{R}^{2})\cap L^{2}(\mathbb{R}^{2}) $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M8">\begin{document}$ f \in L^{1}(\mathbb{R}^{2})\cap L^{p}(\mathbb{R}^{2}) $\end{document}</tex-math></inline-formula> with some <inline-formula><tex-math id="M9">\begin{document}$ p&gt;2 $\end{document}</tex-math></inline-formula>.</p>

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

Sensitivity analysis for Navier-Stokes equations on unstructured meshes using complex variables

AIAA Journal ◽  
2001 ◽  
Vol 39 ◽  
pp. 56-63
Author(s):  
W. Kyle Anderson ◽  
James C. Newman ◽  
David L. Whitfield ◽  
Eric J. Nielsen
Keyword(s):  
Sensitivity Analysis ◽  
Stokes Equations ◽  
Unstructured Meshes ◽  
Complex Variables ◽  
Navier Stokes ◽  
Navier Stokes Equations

Numerical solution of the reduced Navier-Stokes equations for internal incompressible flows

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1603-1614
Author(s):  
Martin Scholtysik ◽  
Bernhard Mueller ◽  
Torstein K. Fannelop
Keyword(s):  
Numerical Solution ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

Data-parallel line relaxation method for the Navier-Stokes equations

AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 1603-1609 ◽  
Author(s):  
Michael J. Wright ◽  
Graham V. Candler ◽  
Deepak Bose
Keyword(s):  
Stokes Equations ◽  
Relaxation Method ◽  
Parallel Line ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Data Parallel
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